Student's simplest distribution

Abstract

In this paper, I note the pedagogical advantages of an existing, but largely ignored, simple symmetric distribution on the real line: Student's t-distribution on 2 degrees of freedom. The t2-distribution has particularly simple forms for its distribution and quantile functions, and these lead to simply calculated values for a whole host of basic properties of the distribution. In addition, distributions of order statistics from the t2-distribution lead to a recently introduced skew t family of distributions.